Potential theory of subordinate killed Brownian motion in a domain

Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

Subordination of a killed Brownian motion in a bounded domain D ⊃ ℝd via an α/2-stable subordinator gives a process Zt whose infinitesimal generator is -(-Δ|D)α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process Zt in a Lipschitz domain D by comparing the process with the rotationally invariant α-stable process killed upon exiting D. We show that these processes have comparable killing measures, prove the intrinsic ultracontractivity of the semigroup of Zt, and, in the case when D is a bounded C1,1 domain, obtain bounds on the Green function and the jumping kernel of Zt.

Original languageEnglish (US)
Pages (from-to)578-592
Number of pages15
JournalProbability Theory and Related Fields
Volume125
Issue number4
DOIs
StatePublished - Apr 1 2003

Keywords

  • Fractional Laplacian
  • Killed Brownian motions
  • Stable processes
  • Subordination

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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